How to install Blender on a Mac so that multiple user accounts have access to it?
Having tried many more things, what finally worked was:

Changing the ACL permissions of the Applications/Blender directory through finder with the 'Get info' option and set use the 'Apply to enclosed items' option in there (cog wheel icon at the bottom, once you've changed a permission setting).

Even though in there I set the specific user to allow read and write (even using 'Apply to enclosed items' before, it did not do the trick. Only when I allowed staff to do this, it worked. Yet that user was not a member of the group 'staff'. So even though this worked, I don't really understand why this worked.